Mathematics – Algebraic Geometry
Scientific paper
1999-01-15
Mathematics
Algebraic Geometry
AMSTeX, 7 pages
Scientific paper
Let $g$ be a complex semisimple Lie algebra with adjoint group $G$. Suppose that $\sigma$ is an involutive automorphism of $g$. Then $\sigma$ induces uniquely an involution of $G$ also denoted by $\sigma$, let $K=G^\sigma$ be a subgroup of $\sigma$-fixed points. Consider a direct decomposition $g=k+p$ of $g$ into eigenspaces for $\sigma$. Then $p$ is a $K$-module. Denote by $a\subset p$ any maximal abelian ad-diagonalizable subalgebra. Consider the ``baby Weyl group'' $W=N_K(a)/Z_K(a)$. Let $\psi: C[p]^K\to C[a]^W$ be a restriction map of algebras of invariants. Then the famous Chevalley restriction theorem states that $\psi$ is an isomorphism. The aim of this paper is prove the following Theorem. The restriction map $\psi: C[p\times p]^K\to C[a\times a]^W$ is surjective.
No associations
LandOfFree
On Chevalley restriction theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Chevalley restriction theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Chevalley restriction theorem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-597642